# What is the best way to display confidence intervals around a proportion?

I was reviewing an article about the effectiveness of a vaccine and it expressed these in % effectiveness = 1 - odds ratio. So far, so good.

But they showed confidence intervals around the %'s, both in text (e.g. 72%, 95% CI = 33.9% to 88.2%) and in a graph of those numbers (they had a bunch of results to display).

It struck me that the CIs are asymmetric (i.e 72-34 = 38, while 88-72 = 16) and this seemed a bit odd, especially for the graph. Should such graphs use log odds which has symmetric CIs?

• Why are asymmetrical confidence intervals odd? Sep 25 '18 at 15:27
• A cute way to visualize CIs for proportions (that suffer from a similar problem -- you want them to be within [0,1] rather than fly around as the asymptotic normality carelessly thinks) is inchworm plots github.com/BiostatGlobalConsulting/inchworm-plots-stata. They show a density function of the approximating distribution which is probably a Beta. Sep 25 '18 at 15:51
• Why not simply ask the authors to explain/substantiate the CIs they used?
– Jim
Oct 2 '18 at 12:05
• More interesting than the CI (which transforms perfectly) and possible asymmetry of that interval (relative to the mean) is the question about the mean (which does not transform correctly). When one computes mean and CI on some scale but presents them on another scale, then the mean becomes ambiguous (is it $E(f(X))$ or is it $f(E(X))$). Oct 2 '18 at 14:53